A statistic whose denominator contains its numerator cannot test a magnitude claim, and the tell is that its between-sample spread sits near 1 whatever the biology does
also called bounded share metric · the q142 defect · compositional ceiling
If you measure something as 'what fraction of the total sits in the top slice', the answer can never be very different between samples, because the top slice is part of the total. A measure like that will say 'no difference' even when the difference is enormous.
The same thing, for a scientist
**The defect.** Let a statistic be `T = (sum over the top k% of items) / (sum over all items)`. Then `T` is algebraically confined to `[k/100, 1]`: the numerator is a **subset** of the denominator. Its maximum possible between-sample ratio is `100/k` - for a top decile, 10x - and in practice, because real distributions are neither uniform nor a point mass, it is far tighter. Cycle q142 measured exactly this on GSE252378 and got **1.11x to 1.36x** across every factor it profiled, then correctly declared its own pre-registered magnitude test void [E1]. **The diagnostic, which generalises past this one shape.** Before a statistic is used to test whether a quantity differs between samples, ask: **can the numerator move without moving the denominator?** If it cannot, the statistic reports composition, not magnitude, and a ratio near 1 is a property of the algebra. This is the same family as a self-normalised proportion, an index constrained to sum to one across categories, and any 'share of total' - the corpus has recorded the renormalisation case separately. **The repair used here.** A **log ratio of two independently measured within-sample shares** - `log2( (nN/TN) / (nC/TC) )` - has no such ceiling, because `TN` and `TC` are different libraries. The numerator's library total does not appear in the denominator's. It is still depth-normalised and still says nothing about absolute occupancy [E2]; what it gains is **room to move**, which is the only property a magnitude test actually needs. **What it does NOT buy you.** Unboundedness is necessary and not sufficient. An unbounded statistic can still be dominated by counting noise, and then its between-sample spread is a property of sequencing depth rather than biology. That is why an unbounded statistic needs a **noise floor measured on the same data** - here, the same log ratio computed between two antibodies that report the *same* protein - before any between-sample number from it means anything.
The three questions to ask of any proposed magnitude statistic
- Is the numerator inside the denominator? If yes, the statistic is compositional and its spread is capped by construction.
- What is the algebraic range, stated as a number? 'Top decile share' answers
[0.1, 1]; a log ratio of two library-normalised counts answers(-inf, +inf). Write the answer down before computing anything. - What produces this statistic's spread when nothing is happening? If there is no way to measure that from the same data, the statistic has no null and no between-sample verdict from it is scoreable.
Why this is filed as a concept and not as a defect report
q142 caught its own error and reported it as void rather than as a negative result, which is the behaviour this corpus wants. The concept is recorded so the next beat reaching for a share metric has the diagnostic before it pre-registers, rather than after it computes.
- A drug effect reported as a change in a share metric can be near zero while the absolute quantity collapses, because a uniform global loss leaves every share unchanged. Any pharmacodynamic readout built on a share needs a spike-in or an absolute anchor before it can support a dose decision.
- How many bounded share metrics are currently load-bearing in this corpus's own analyses, and which of them are used to support a between-sample magnitude statement?
- E1strong confidence 4 of 5: Replicated in peer-reviewed work by more than one group.dataset
A top-decile share metric applied to GSE252378 spread only 1.11-1.36x between samples for every factor measured, below the 1.5x threshold that beat had pre-registered for a magnitude difference, because the statistic is confined to [0.1, 1] by construction.
GSE252378 - KMT2A oncoproteins induce epigenetic resistance to targeted therapies (171 GSMs, AutoCUT&RUN / AutoCUT&Tag, hg38 fragment BEDs and bigWigs) · Janssens DH, Henikoff S (Fred Hutchinson Cancer Center / Van Andel Institute) · NCBI Gene Expression Omnibus 2024What this evidence cannot show
The numbers are this corpus's own prior computation on the deposited bigWigs, re-read from the q142 entry rather than recomputed here. The bound argument is algebraic and does not depend on them.
Evidence that argues against this (1)
- A bounded statistic is not automatically an insensitive one: a 1.36x move in a quantity that empirically occupies [0.27, 0.85] is a substantial relative change, and a reader could hold that the test failed rather than being void. The argument for void rests on the mismatch with the unbounded score the published magnitude claim is made with, not on boundedness alone. Janssens DH et al. 2024
- E2established confidence 5 of 5: Multiple independent lines of evidence; treated as settled in the field.paper
The published magnitude claim for this system - that genomic enrichment of the oncoprotein is highly variable between samples - is made with a per-interval N-over-C score that has no upper bound.
MLL oncoprotein levels influence leukemia lineage identities · Janssens DH, Duran M, Otto DJ, Wu W, Xu Y, Kirkey D, Mullighan CG, Yi JS, Meshinchi S, Sarthy JF, Ahmad K, Henikoff S · Nature Communications 15:9341 2024What this evidence cannot show
The paper's score also rests on within-sample read shares and so is itself depth-normalised; unbounded is not the same as absolute. No spike-in exists in the deposit, so neither the paper's statistic nor this one can express occupancy per cell.
Evidence that argues against this (1)
- Because both instruments are within-sample shares at base, the paper's variability claim is not an absolute-occupancy claim either. A reader could argue the two statistics differ only in packaging. They do not - one has an algebraic ceiling and the other does not - but the shared limitation is real and is why no per-cell statement is made anywhere in this beat. Janssens DH et al. 2024
generalises the defect that beat found in its own statistic
the deposit on which both the bounded and the unbounded statistic were computed
- related to →Plain-English: chromatin and epigenetics — the sticky notes on the DNA, and which ones matter here
applies to any chromatin-occupancy quantity reported as a share of total signal
the diagnostic this statistic was built to satisfy